Helping Students to Think Mathematically

What does it mean to think mathematically?  

It means using math vocabulary, language and symbols to describe or interpret mathematical concepts, procedures and to discover relationships among ideas.  Therefore when a student problem solves, they use previous knowledge, skills, and understanding of concepts to solve a problem.  This process might include formulating problems, applying a variety of strategies, or interpreting results.

What can we do to help our students become better mathematical thinkers?  

We can teach and model problem solving strategies.  We can remember and plan our lessons to involve the three stages of conceptual development: concrete, pictorial, and abstract. We can have the students talk or write about how they got an answer either with the class or with a partner.  We can use writing in the mathematics classroom (such as math journals) to allow the students to practice expository writing and show their understanding.  We can exhibit math word walls and have the students use the glossary in their book to write and define terms. 

We can also create a positive and safe classroom atmosphere for problem solving... 

By being enthusiastic and allowing the students to take risks without consequences.  By emphasizing the process as well as the answer, the students may be willing to try unconventional or different ways to solve the problem.  I always tell my students that there isn't just one right way to get an answer which surprises many of them.  In fact, this is one of the posters that hangs in my classroom.

  

As math teachers, let's continue to emphasize problem solving so that all students will acquire confidence in using mathematics meaningfully. But most of all, let's have fun while we are doing it!



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If you are interested in having a math dictionary for your students, check out A Simple Math Dictionary. It is a 30 page student dictionary that uses easy and clear definitions as well as formulas and examples so that students can learn and understand new math words without difficulty or cumbersome language. Most definitions include diagrams and/or illustrations for the visual learner. Over 300 common math terms are organized alphabetically for quick reference.

Defeating Negative Self-Talk

One of the biggest problems with the college students I teach is their math anxiety level. Math anxiety is the felling of tension and anxiety that interferes with the manipulation of numbers and the solving of math problems during tests. In other words - mathphobia! This is a learned condition, not something they are born with and is in no way related to how smart a student is. In my Conquering College class, we have been looking at causes for anxiety which include bad experiences, teacher and/peer embarrassment and humiliation, or being shamed by family members. We've been looking at ways to reduce math anxiety such as short term relaxation as well as long term techniques and managing negative self-talk.

For many of my students, a song is the best way of remembering. I found an old nonsense song by Roger Miller entitled, You Can't Roller Skate in a Buffalo Herd. First we read over the words. Next we watched a video on You Tube and then we actually sang the song. I replaced the words "But Ya can be happy if you've a mind to" with "But ya can be positive if you put your mind to it."

You Can’t Roller Skate in a Buffalo Herd

By Roger Miller

Ya can’t roller skate in a buffalo herd,

Ya can’t roller skate in a buffalo herd,

  Ya can’t roller skate in a buffalo herd,

*But ya can be positive if ya put your mind to it.

 Ya can’t take a shower in a parakeet cage,

 Ya can’t take a shower in a parakeet cage,

 Ya can’t take a shower in a parakeet cage,

 *But ya can be positive if ya put your mind to it.

All ya gotta do is put your mind to it,

Knuckle down, buckle down,

Do it, do it, do it!

Well, ya can’t go swimmin’ in a baseball pool,

Well, ya can’t go swimmin’ in a baseball pool,

Well, ya can’t go swimmin’ in a baseball pool,

 *But ya can be positive if ya put your mind to it.

Ya can’t change film with a kid on your back,

Ya can’t change film with a kid on your back,

Ya can’t change film with a kid on your back,

 *But ya can be positive if ya put your mind to it.

Ya can’t drive around with a tiger in your car,

Ya can’t drive around with a tiger in your car,

Ya can’t drive around with a tiger in your car,

*But ya can be positive if ya put your mind to it.

All ya gotta do is put your mind to it,

Knuckle down, buckle down,

Do it, do it, do it!

Well, ya can’t roller skate in a buffalo herd,

Ya can’t roller skate in a buffalo herd,

Ya can’t roller skate in a buffalo herd,

 *But ya can be positive if ya put your mind to it.

Ya can’t go fishin’ in a watermelon patch,

Ya can’t go fishin’ in a watermelon patch,

Ya can’t go fishin’ in a watermelon patch,

*But ya can be positive if ya put your mind to it.

 Ya can’t roller skate in a buffalo herd,

 Ya can’t roller skate in a buffalo herd,

  Ya can’t roller skate in a buffalo herd,

  *But ya can be positive if ya put your mind to it.

So how did the lesson go? Let's just say that my college students were having so much fun singing the song that the secretary had to come and shut our classroom door. And the response from the students the next day, "I can't get that song out of mind!" Maybe negative self-talk has finally met its match!